1 
Computational methods in permutation group theoryAlAmri, Ibrahim Rasheed January 1993 (has links)
In Chapters 2 and 3 of this thesis, we find the structure of all groups generated by an ncycle and a 2cycle or a 3cycle. When these groups fail to be either Sn or An then we show that they form a certain wreath product or an extension of a wreath product. We also determine, in Chapters 4 and 5, the structure of all groups generated by an ncycle and the product of two 2cycles or a 4cycle. The structure of these groups depends on the results obtained in the previous chapters. In Chapter 6 we give some general results of groups generated by an ncycle and a kcycle. In Chapter 7 we calculate the probability of generating a proper subgroup, other than the alternating group, by two elements one of which is an ncyc1e and the other is chosen randomly. In Chapters 8 and 9 we give some of the programs written in GAP language, which used in the earlier work and which can be used by other workers in this area.

2 
Supergravity in superspace : supergeometry, differential forms and algebraic structureGreitz, Jesper January 2012 (has links)
The following thesis will be concerned with various aspects of supergravity theories in a superspace setting, focusing mainly on maximal and halfmaximal theories in three dimensions and maximal theories in tendimensions. For the threedimensional theories it is convenient to start from an offshell superconformal geometry valid for any number of supersymmetries. We first apply this formalism to show that it is consistent to couple ABJM and BLG theory to conformal supergravity, in doing so we find that N = 8 superconformal matter can also be charged under the gauge group SO(N). By imposing further constraints on the offshell superconformal geometry, we obtain halfmaximal and maximal Poincare supergravity. We solve for the geometry at dimension one in the halfmaximal case with sigma models of the form (SO(8) x SO(n))\SO(8, n), and for the complete geometry in the maximal theory, where the scalar fields live in the coset SO(16)\E8. Using the Ricci identity, we also derive the equations of motion for the scalar and fermion fields in the latter theory. Using supersymmetry and duality we derive the form spectrum of the above Poincare supergravity theories and of type IIA and IIB supergravity in ten dimensions. Particular we show that the consistent Bianchi identities, which are not guaranteed to be satisfied from cohomology, determine a Lie super coalgebra. We derive the Cartan matrices of the dual algebras which are Borcherds algebras. The Cartan matrices can be used to generate the entire form field spectrum. We study gaugings of halfmaximal and maximal Poincare supergravity in three dimensions by introducing a nonabelian gauged subgroup of the duality group and making use of the gauged MaurerCartan form. The differential forms can also be studied in the gauged theory by deforming the Bianchi identities. The closure of the full system of forms requires the presence of D + 2form field strengths in the supergravity limit. In superspace, the Borcherds algebras predict an infinite number of form fields of degree larger than that of spacetime. Indeed all those of degree larger than D + 2 are zero in supergravity, although this might change in string theory. We provide some evidence that a sixform, in halfmaximal supergravity in three dimensions can become nonzero in the presence of α'corrections.

3 
Algebraic 2complexes over certain infinite abelian groupsEdwards, T. January 2006 (has links)
Whitehead's Theorem allows the study of homotopy types of two dimensional CW complexes to be phrased in terms of chain homotopy types of algebraic complexes, arising as the cellular chains on the universal cover. It is natural to ask whether the category of algebraic complexes fully represents the category of CW complexes, in particular whether every algebraic complex is realised geometrically. The case of two dimensional complexes is of special interest, partly due to the relationship between such complexes and group presentations and partly since, as was recently proved, it relates to the question as to when cohomology is a suitable indicator of dimension. This thesis has two primary considerations. The first is the generalisation to infinite groups of F.E.A. Johnson's approach regarding problems of geometric realisation. It is shown, under certain restrictions, that the class of projective extensions containing algebraic complexes may be recognised as the unit elements of a ring, with ring elements congruence classes of extensions of the trivial module by a second homotopy module. The realisation property is shown to hold for the free abelian groups on two and three generators, and for the product of a cyclic group and a free group on a single generator. Secondly, a reinterpretation is given of the well documented relation ship between the congruence classes represented by Swan modules and the projective modules constructed via Milnor's connecting homomorphism and the relevant fibre product diagram. This relationship is shown to be typical of projective modules occurring in extensions of a twosided ideal by a quotient ring, and we show that any twosided ideal in a general ring results in a MayerVietoris sequence which is different and complimentary to the standard excision sequence.

4 
On stable categories of group algebrasPoulton, Andrew January 2014 (has links)
We study the stable category of a group algebra AG over a regular ring A, for a finite group G. We construct a right adjoint to the inclusion of the stable subcategory of Aprojective AGmodules into the full stable category. We use this functor to study the stable category of VGlattices, where V is a complete discrete valuation ring. We focus on HelIer lattices, the kernels of projective covers of torsion OGmodules. If k is the residue field of 0, we show that the Heller lattices of the simple kGmodules generate a dense sub category of the stable category laUOG of OGlattices. Turning to more general kGmodules, we show that the stable endomorphism ring of the Heller lattice of a kGmodule M is isomorphic to the trivial extension algebra of the stable endomorphism ring of M when 0 is ramified, generalising a result due to S. Kawata. We conclude by discussing the structure of a connected component of the stable AuslanderReiten quiver containing the Heller lattice of an indecomposable kGmodule. We also give necessary and sufficient conditions for the middle term of the almost split sequence ending in a virtually irreducible lattice to be indecomposable

5 
Generalized piece groups and the Greendlinger lemmasCramp, Gerald Anthony January 1972 (has links)
No description available.

6 
Almost commuting elements of real rank zero C*algebrasKachkovskiy, Ilya January 2013 (has links)
The purpose of this thesis is to study the following problem. Suppose that X,Y are bounded selfadjoint operators in a Hilbert space H with their commutator [X,Y] being small. Such operators are called almost commuting. How close is the pair X,Y to a pair of commuting operators X',Y'? In terms of one operator A = X + iY, suppose that the selfcommutator [A,A*] is small. How close is A to the set of normal operators? Our main result is a quantitative analogue of Huaxin Lin's theorem on almost commuting matrices. We prove that for every (n x n)matrix A with A ≤ 1 there exists a normal matrix A' such that AA' ≤ C[A,A*]¹/³. We also establish a general version of this result for arbitrary C*algebras of real rank zero assuming that A satisfies a certain indextype condition. For operators in Hilbert spaces, we obtain twosided estimates of the distance to the set of normal operators in terms of [A,A*] and the distance from A to the set of invertible operators. The technique is based on Davidson's results on extensions of almost normal operators, Alexandrov and Peller's results on operator and commutator Lipschitz functions, and a refined version of Filonov and Safarov's results on approximate spectral projections in C*algebras of real rank zero. In Chapter 4 we prove an analogue of Lin's theorem for finite matrices with respect to the normalized HilbertSchmidt norm. It is a renement of a previously known result by Glebsky, and is rather elementary. In Chapter 5 we construct a calculus of polynomials for almost commuting elements of C*algebras and study its spectral mapping properties. Chapters 4 and 5 are based on author's joint results with Nikolay Filonov.

7 
2selmer parity for Jacobians of hyperelliptic curves in quadratic extensionsMorgan, Adam John January 2015 (has links)
We study the 2parity conjecture for Jacobians of hyperelliptic curves over number fields. Under some mild assumptions on their reduction, we prove it over quadratic extensions of the base field, providing essentially the first examples of the 2parity conjecture in dimension greater than one. The proof proceeds via a generalisation of a formula of Kramer and Tunnell relating local invariants of the curve, which may be of independent interest and works for positive characteristic and characteristic zero local fields alike. Particularly surprising is the appearance in the formula of terms that govern whether or not the CasselsTate pairing associated to the Jacobian is alternating, which first appeared in a paper of Poonen and Stoll. We prove the formula in many instances and show that in all cases it follows from standard global conjectures.

8 
An activity theory analysis of linear algebra teaching within university mathematicsThomas, Stephanie January 2012 (has links)
The focus of my research was to explore the teaching of linear algebra to a large group of mathematics undergraduates (> 200). With this thesis I present a characterisation of a university mathematics teaching practice in the context of linear algebra. The study took place over a twelve week period, one academic semester, at a UK university with a strong tradition in engineering and design technology. Two researchers working closely with a mathematician, the lecturer of linear algebra, collected data in interviews with the lecturer, and in observations of his lectures (which were audiorecorded). Students' views were sought via two questionnaires and focus group interviews. Data analysis was largely qualitative. Linear algebra is an introductory module in most standard rst year undergraduate degree courses in mathematics. Research shows that students nd the highly conceptual nature of linear algebra very di cult and challenging. The lecturer, a research mathematician, had redesigned the linear algebra module based on his own experience of students' di culties with the topic in the previous year. He followed an inductive approach to teaching instead of a more traditional DTP (de nitiontheoremproof) style. He based his teaching on informal reasoning about examples that were designed to engage students conceptually with the material. Through this research I gained insight into the lecturer's motivation, intentions and strategies in relation to his teaching. In applying an activity theory analysis alongside a traditional grounded theory approach to my research, I conceptualised the lecturer's teaching practice and presented a model of the teaching process. This takes account of the lecturer's didactical thinking in planning and delivering the linear algebra teaching. Findings from the study give insight into the educational practice of a mathematician in his role as a teacher of university mathematics. I present some of the outcomes of the study in terms of mathematics (three linear algebra topics  subspace, linear independence and eigenvectors), in terms of the didactics of mathematics and in terms of the theoretical basis of Mathematics Education as a discipline.

9 
Solution of the world problem for certain types of groupsBritton, John Leslie January 1954 (has links)
No description available.

10 
Numerical methods applied to trace and explicit formulaeDwyer, Jo January 2014 (has links)
In this thesis, we use numerical methods in conjunction with trace or explicit formula to obtain various number theoretical results. The main results are: the derivation of an explicit version of the trace formula that will enable us to compute the lowlying eigenvalues of the spectrum of all congruence subgroups ┌o(N,X) for nonsquarefree level, N, and even Dirichlet character, X; we prove new cases of the Artin Conjecture for S5Artin Representations; we prove an upper bound for ranks of highranked elliptic curves. We also use the numerical method of computing an optimal testfunction for explicit formulae to investigate the relationship between the rank and zerorepulsion of Lfunctions corresponding to elliptic curves

Page generated in 0.0277 seconds